Force, Mass and Acceleration

We have seen that:

If the mass (of the trolley) is constant and the applied force is increased, then the acceleration __________.

If the applied force is constant and the mass (of the trolley) is increased then the acceleration __________.

We can say that the acceleration is proportional to the Force and inversely proportional to the mass.

This can be written mathematically as follows:

a ∝ F

a ∝ 1 m

We can combine these two proportionalities as follows:

a	∝	F
		m

and rearrange to form:

F ∝ ma

The units of force are __________. One __________ is defined as the force required to give a __________ of 1kg, an __________ of 1m/s². So our proportionality becomes an equality as follows:

F = ma
where	F	=	Force in Newtons, N
	m	=	Mass of the object in Kilograms, kg
	a	=	Acceleration of the object in metres per second per second, m/s/s or m/s2 or ms-2

This can be summarised in the following 'magic triangle':

We have seen that to get a greater rate of change of speed, we need a __________ force. It is also true to say to get a greater rate of change of direction, we need a __________ force. Turning a sharp corner or tight bend requies a larger force as the __________ changes faster. This is why it is more precise to say acceration is the rate of change of __________, rather than __________.

Racing drivers take the 'racing line' to minimise rate of change of direction. This allows them to carry the maximum amount of speed through a corner for the grip the have left on the tires. Try and turn too quickly and the tires won't be able to provide the force requied, and the car will leave the track!

• Find out more about the racing line at Kart City